# Propeller Selection For Boats and Small Ships

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2 E Marine Training - Prop Matching - February, Propeller Anatomy Efficiency of Propulsion How Props Work Physical Characteristics Hydrodynamic Characteristics Hydrodynamic Equations Cavitation Hull Effects Advanced Prop Design This course first discusses the basic elements of efficiency of propulsion of any type, not only marine propellers but any sort of propulsion other than rockets, since the basic principles apply to any sort of propulsion system that does not carry its own reaction mass. Then the specifics of how a propeller works, will be discussed, and we will look at the physical characteristics of propellers, the hydrodynamic characteristics of propellers, and the equations or formulas needed to calculate specific aspects of propellers to allow us to predict their efficiency, thrust and so on. The actual equations won t be derived in this course, due to the limited time, but some explanation will be give about where they come from and how they work. If you are interested in the derivations of the equations, please refer to the references. Note especially that Saunders, Hydrodynamics of Ship Design, available from the Society of Naval Architects and Marine Engineers, or by interlibrary loan, is a very complete, and highly readable book, (actually three volumes) and though it is expensive, and perhaps a bit dated (written in the 50 s) it presents a very good discussion and background, without too much mathematics, of virtually every aspect of hydrodynamics as might be applied to ships, yachts and even fish. This text probably represents at least a good beginning point for anyone seriously interested in understanding hydrodynamics of marine vehicles. We will then discuss cavitation, the effects of the hull on the propeller and the propeller on the hull that have to be taken into account to select propellers, and then comment shortly on advanced propeller design so that you will have a bit of an idea of what sort of advances are potentially available for special problems.

3 E Marine Training - Prop Matching - February, Propeller Selection Engine - Prop Matching Strategy Computer Programs Resistance Calculation Trial Data Shaft Angle/Strut Drag/Clearance Vibration Nozzles Surface Piercing Props/Jets The basic goal of selecting a propeller is to get the hull, engine and propeller matched to achieve the desired goals in terms of speed, possibly towline pull, thrust and engine loading. This requires some thinking about the overall mission of the boat, and understanding of how the propulsions system should perform overall, not only from an engineering standpoint but from an economic one as well. There are many techniques for matching propellers, most developed prior to the use of computers, but we will discuss only two, which are related, and in fact, will only use one. The older techniques use various graphs and so forth, but the method implemented in the computer spreadsheets given here is the current standard, and probably the most accurate available, at least for standard type propellers. We will discuss resistance calculation in enough detail to understand the problem in general and to use the two methods of resistance given that are specific to many small craft. Most commonly, we will find ourselves working with existing vessels, either to correct problems, or to modify the equipment or service of a boat, such as when it is re-powered. This allows us to get the needed information on resistance by running trials, and then back-calculating resistance. We will discuss the issue of shaft angle, strut drag, and clearance, and a bit about shaft and system vibration, since these often are part of the issue in problem props. Finally, we will discuss the application of nozzles in props and quickly cover surface piercing propellers and water jets.

4 E Marine Training - Prop Matching - February, Efficiency Propulsion Works by Grabbing And Throwing Mass Thrust = m v - but - Energy = 1/2 m v 2 Lowest Thrust per Pound of Water - Best Efficiency Output Velocity Greater than Zero is Wasted Efficiency Depends on Frontal Area Prop Ideal Efficiency Higher as Pitch Gets Higher - More Mass Flows Through - Thrust Load Goes Down Ideal Efficiency Based on Thrust/Speed, Area Device Efficiency - No Device Produces Thrust Perfectly Best Props Typically Produce 80% of Input Power As Water Flow - Best Jets Maybe 90% In general, all propulsion works by throwing mass in the opposite direction you want to go, which, by Newton s law produces and equal and opposite reaction of you moving. The thrust you produce is the mass times the speed you throw it away. (Note that pounds are units of force, not mass - the proper English units of mass are slugs, which incidentally weigh about 32 pounds. A kilogram is also a mass, not a force. The metric unit of force is the Newton. Weight is the force a mass produces due to gravity, which is why it s confusing.) All propulsion works this way; even when walking you are grabbing the earth with your feet and pushing it backwards away from you. However, the earth is so massive compared to you, only you seem to move. All propulsion, except rockets (which carry their reaction mass) also takes in mass from the environment, increases its speed to that of the vehicle, then a bit more, and throws it away. Let's first consider a propeller as just a magic device that grabs and moves water, to see what we can learn without going into detail. To propel boats, we grab water and throw it aft. Thrust is mass times velocity, but the energy required to throw it is one half mass times velocity squared. The more water we grab, the less thrust we need per pound of water so that we can throw it slower with less energy, producing more efficient propulsion. There are then two ways of grabbing a lot of mass, either by moving through the water fast, or by having a large area scoop or whatever, to grab it with. The ratio of thrust to speed, area and water density is expressed as "thrust load coefficient", C tl, which can be proven to determine the maximum or ideal efficiency η i of any propulsor: η i = 2 / ( 1 + (C tl + 1)1/2 with C tl = Thrust / 0.5 ρ A V a 2 ρ, rho, is water density, A is area, V a is the speed of the device through the water. Thrust load coefficient is simply the ratio of thrust to the weight of water that passes through the device per second times half the speed it passes through. Since no real device is perfect at accelerating water, real world efficiency is less that the ideal.

5 E Marine Training - Prop Matching - February, Thrust Load Diagram Thrust Load Is The Main Limit Of Efficiency 100% 90% Ideal A nd Typical Efficiency M aximum Ideal Typical Propeller M ax imum T ypical Real Prop Efficiency 80% P/D 1.2 Efficiency 70% 60% P/D 0.8 P/D % 40% 30% P/D 0.6 Higher Boat Speed or Larger Device Areas = More Mass Flowing through Device Thrust Load Coefficient Ctl = Thrust / 0.5ρAVa 2 This figure shows ideal efficiency plotted against thrust load factor with the actual efficiency of some typical props. The plot also has a constant line at 80% of ideal efficiency, which is the typical limit for propellers. This is sometimes called device efficiency and is the measure of how good a device is at moving water. Incidentally, this figure does not have anything about water in it, and applies equally well to air propellers, but air is much less dense than water, so ρ is small. There is nothing specific about propellers in this plot. It applies equally well to waterjets, oars, paddlewheels or any other forms of fluid propulsion (provided we can identify the area of the device. Some devices may have higher (water jets or some types of sculling hydrofoils - also known as penguin propulsion can be a bit higher) or lower (paddlewheels and oars have about 50%) device efficiencies, but we can calculate their approximate efficiency from this plot This plot shows that thrust load factor is the most important factor for efficiency. The larger the propulsor, (and usually the slower it turns), and the faster it goes through the water, the better the efficiency, though there are other limits on diameter, not only practical limits such as draft, but secondary propeller effects that limit the efficiency of large props. The plot also shows this. If we don t accelerate the water at all, we spend no energy, but get no thrust. This is theoretically very high efficiency, but gets nothing, and since in reality, no device is perfect there is a limit to maximizing the area of the device.

11 E Marine Training - Prop Matching - February, Prop Hydrodynamic Equations I Thrust Coefficient: K t = Thrust / ρ D 4 n 2 Torque Coefficient: K q = Torque / ρ D 5 n 2 Advance Ratio: J = V a / n D Cavitation Numbers ρ D n V a P t σ 0.7r = P t / ( 1 / 2 ρ (V 2 a + (0.7 π n D) 2 ) τ crit = Thrust / ( 1 / 2 A p (V 2 a + (0.7 π n D) 2 ) Propeller Efficiency (Measured in Open Water) η o =(J/2π) (K t / K q ) A p σ 0.7r τ crit Symbols (English Units) Water Density, Ft-Lbs/s Propeller Diameter, Ft Propeller Rev/Sec Prop Speed of Advance, Ft/s Vapor Pressure At Prop, Lbs/Ft 2 ( * Hub Submergence, Ft) Projected Prop Area, Ft 2 Cavitation 70% r Critical Thrust Coefficient It is possible to calculate the flow over the propeller surface directly with very sophisticated computer programs, but most boat propellers are basically similar, so you can use test data instead. You can test a propeller in a water tunnel at different combinations of water and shaft speeds, measuring torque, thrust and efficiency as a function of advance ratio, J. The "thrust coefficient" (Kt) is the ratio of thrust to shaft speed, diameter and water density. "Torque coefficient" (Kq) is a similar ratio for torque. Both these factors vary with advance ratio and depend on the prop characteristics, but the tests allow us to plot them or fit them to statistical calculations. Once we know the thrust or torque coefficient for a given J, we can then calculate the thrust produced by the prop or the torque required to spin it at a certain speed. (Torque or thrust is just the coefficient times the factors in the denominator.) Cavitation number is based on the ratio of the water pressure at the propeller hub to the characteristic pressure produced by the speed of water. Various speeds are used, but in this case, we will use the speed at the section 70% of the radius away from the shaft centerline, since this is often considered to represent the average conditions on the propeller. Remember that this speed is the sum of the forward speed and the speed due to the revolution of the prop. We can develop another cavitation related measure based on the thrust the propeller is producing divided by the projected area times the characteristic pressure due to speed. Since thrust divide by area is a pressure this will help us to determine limits of thrust based on cavitation. Efficiency is the ratio of thrust and speed to torque, so it is determined by Kt, Kq and J. Efficiency, Kt, and Kq are usually plotted against J for a range of pitches for one style propeller. Note again that theses ratios are non-dimensional. These ratios are used instead of actual RPM, speed, thrust and torque so that they are easily scaled to whatever size and speed prop is required.

13 E Marine Training - Prop Matching - February, Prop Hydrodynamic Equations II Thrust Coefficient (Fit To Test Data) K t = Σ C Ti J si P/D ti EAR ui Z vi Torque Coefficient (Fit To Test Data) K Q = Σ C Qi J si P/D ti EAR ui Z vi Blount - Fox Thrust Criteria: K t / J 2 = R T / ( ρ D 2 v a2 ) - This is a method to find RPM if you know resistance, speed and diameter - the equation eliminates RPM. You calculate curves of efficiency, etc. by K t / J 2 and can then optimize them and pick the point where you get the right K t / J 2, then calculate required RPM from J. Similar equations can be developed to find any other factor. Square of Velocity at 70% r v 0.7r = (J / J 2 )v 2 The obvious question is where to get the thrust and torque coefficients if we can t do propeller tests. There are several sets of data based on statistical analyses of many tests. Each of these sets has been fit to a very messy pair of equations by extensive computer analysis. The equations say that the coefficient is the sum of up to 47 terms. Each term is an arbitrary constant times advance ratio, J, to an arbitrary power, times pitch to diameter ratio, P/D, to another arbitrary power, times EAR to a third arbitrary power, times Z to a fourth arbitrary power. There is a different equation for Kt and Kq, and different tables of constants and powers for different types of propellers. Though these equations are very messy, they don t have to be algebraically manipulated in any way. You only have to plug in your J, P/D, EAR and Z, multiply and add. This would be quite tedious by hand, but it s a snap on a computer, even with a spreadsheet. Incidentally, the equations are a statistical fit to data and don t necessarily make sense on their own, or outside the range of data that was used to develop them. It is interesting to enter nonsense such as one or zero bladed propellers or negative pitch ratios and see what comes out, but this is a reminder that the equations are not valid outside of the data that was used to generate them. Another equation that is frequently useful, though not used in this course, is the Blount-Fox thrust criteria. This is produced by dividing thrust coefficient by J squared and substituting and simplifying. The result is a coefficient that can also be produced by dividing thrust by density, diameter and speed. The merits of this coefficient is that RPM doesn t enter the equation, so that you can determine some propeller factors before you know RPM, then solve for RPM. Blount and Fox produced charts of this factor for typical small craft propellers, to reduce the effort of hand calculations and it remains a useful technique for early design, and solving some specific problems. However, the speed of computer methods allows you to beat the problem to death by just guessing at RPMs repeatedly using the standard equations. Another factor, the square of velocity at 70% radius (which is used in the cavitation equations) can also be determined in terms of J alone (the resulting number is the same). This appears in some methods, and though not used in this course is included for completeness.

15 E Marine Training - Prop Matching - February, Standard Cavitation Diagram Plot σ 0.7r Versus Log(τ crit ) and Compare Against Standard Criteria % Back Cavitation Cavitation Criteria 0.7 5% Back Cavitation 10% Back Cavitation Blount-Fox 10% Line % Back Cavitation 30% Back Cavitation 0.5 Cavitation Log(τcrit) σ(0.7r ) The standard criteria for small ship and boat (especially planing boat) cavitation was also developed by Blount and Fox based on the GAWN and Newton Rader data. The light lines show various percentages (in terms of area covered by bubbles) of back cavitation. The two axes are the cavitation number at 70% radius and the log of the critical thrust factor. The dark line is a linear fit to roughly ten percent back cavitation, which is the level at which cavitation is considered to begin to be important. This line is when: τ c = σ 0.7R 0.88 Once τ c exceeds this factor, the propeller will be seriously cavitating, and you may have to take steps to fix the problem. In general, these steps will be to increase the DAR/EAR or to decrease the speed of the blades, which might require increasing the pitch. There are several other cavitation related factors, notably the thrust and torque for fully cavitating conditions. These are coded on the spreadsheets, but are not really worth discussing. Note that this is a standard simple method for evaluating cavitation. More sophisticated methods, including model tests and direct simulation with very sophisticated computer programs are available when appropriate, but these methods are beyond the scope of this course and should be referred to specialists in propeller design. It is also worth noting that there are tables/formulas for performance of cavitating standard propellers, but again, the goal is to avoid cavitating conditions.

16 E Marine Training - Prop Matching - February, Wake Fraction And Thrust Deduction Hull Affects Prop - Prop Affects Hull Wake Fraction - 1-W t : Slower Flow Into Prop Due To Hull 6 0 Shaft: Semi-Planing & Planing 100% - 96%, 12 0 Shaft: Semi-Planing & Planing 97% - 95%, Slow Displacement - Twin Screws: 90%, Single: 80% Outboards, Outdrives: 97% Thrust Deduction - 1-t: Lost Prop Thrust: Hull, Rudder 6 0 Shaft: Semi-Planing & Planing 98%-99%, 12 0 Shaft: Semi-Planing & Planing 98% - 99%, Slow Displacement - Twin Screws: 92%, Single: 85% Outboards, Outdrives: 100% Both Depend On How Much Hull In Front Of Prop, Rudder Most propellers operate behind the hull of a boat, but standard thrust and torque tests are run with the propellers operating in clear water in a tunnel. (The mechanism supporting and turning the propeller is behind it.) You have to correct for the effect of the hull on the propeller. The hull slows down the water entering the prop. The percentage the boat slows down the water is called "wake fraction". Typical planing and semi-planing boats have a wake fraction less than 5%, so a boat may be going 20 knots, but the propeller seems to go a bit over 19 knots. The water near the boat is being dragged along at about one knot. Strictly speaking, there two wake fractions, one for thrust and one for torque, but these two factors are generally quite close, so you can usually assume they are the same. The suction of the propeller also adds drag to the boat hull so it doesn't really produce as much useful thrust as it would in a water tunnel test. This is called "thrust deduction", and is also about 5% for planing boats. Both factors depend on shaft angle. Some hulls also make the flow into the propeller rotate. This makes the propeller acts as if it was spinning slower or faster and is called "relative rotational efficiency". There are even devices that do this intentionally to improve efficiency, especially for large ships, but in most boat hulls, this factor is unity. There is no one simple method of estimating wake fraction and thrust deduction for all hulls but there are estimating techniques and typical data available for most boat types. These factors are best found from trials data. Even if you are not exact, the trial data will tend to cancel out the effects. For a first cut, you can use 10%-20% for wake fraction and thrust deduction for most displacement type hulls like trawler yachts or sailboats with the propeller in a cutout in the keel, 10% for sailboats with fin keels and a prop on a strut and 0%-5% for most planing boats. Multiply the speed by one minus the wake fraction. This is the "velocity of approach", Va, the speed the prop actually sees. It is also worth checking to see how much difference it makes, by checking a range of values.

17 E Marine Training - Prop Matching - February, Hull Efficiency, Relative Rotational Efficiency, Quasi-Propulsive Efficiency Hull Efficiency: η h = η r (1-t) / (1-W t ) Boat Uses Power Based On Boat Speed, V Non-Propelled Resistance, R T (With Appendages, Air) Prop Produces Power Based On V a =(1-w)V Prop Produces Thrust Based On T = R T / (1-t) Relative Rotational Efficiency: η r Due to Swirl Into Prop Typically Small: 101% - 97%, Quasi Propulsive Efficiency: η D = η o η r (1-t) / (1-W t ) η D =EHP / Delivered HP = (R T V / T V a ) * η o η r May or May Not Include Gearset, Shaft Losses (~3%) Since hull efficiency and other terms are frequently used, it s important to understand them. The effect of the propeller in slowing down flow into the propeller acts to reduce the power the propeller puts out because power is force times speed. However, if the propeller has to produce extra thrust (because of thrust deduction) to push the boat through the water, this is a loss. Finally if the flow around the hull acts in some way to change the propeller efficiency there are more potential losses or gains. In one way, these factors might be considered an accounting issue, since all of these factors come from the effort to predict power requirements from model tests run in specific standardized ways. Unfortunately, there is no source for small scale water. You have to use regular water, and its viscosity (stickiness) is proportionately larger than it would be at full scale. Thus effects due to viscosity are larger at small scale, and they have to be corrected for by subtracting out calculated small scale viscous effects (mainly skin friction) and then adding back calculated large scale effects. The result of this is that the force to move a full size vessel that weighs say 100,000 pounds is less than 1000 times that of a model that weighs 100 pounds. Traditionally, initial resistance model tests are run unpowered, and also often without appendages like struts and shafts. Sometimes actual measurements of flow velocities in the propeller area are made during these tests to help determine wake fraction. If a series of self-propelled tests is run, the model is also pulled to make up the additional drag caused by small scale and the scale speed of the propeller is noted. The various thrust deductions, wake fractions and so on are then determined from the various scaling adjustments to this process, and these interaction factors essentially get the books to balance out. Thus we have a hull efficiency that expresses the effect of wake fraction and thrust deduction on the efficiency of propulsion, and then a quasi-propulsive efficiency that takes into account everything except bearing and gear losses (sometimes sometimes they are included make sure you know what is meant - the difference is about 3%). For most boats, this is about 55% of less, so ultimately, you have to buy about twice the engine as the hull alone requires with perfect propulsion.

19 E Marine Training - Prop Matching - February, Engine - Prop Matching Thrust Must Equal Drag Engine Torque Equals Shaft Torque Engine Speeds/Slows to Match Torque Boat Speeds/Slows to Match Thrust Power Reduced If Prop Can't Make Turns J Increase, Torque Increases, Engine Slows Further Major Problems - Wasted Power, Damaged Engines - Particularly With Turbochargers The engine and gear produce torque that spins the shaft. The propeller spins and produces thrust, which overcomes drag to produce speed. Available engine torque depends on the engine, fuel flow, gear ratio, and engine RPM. Required propeller torque depends on RPM, propeller design, and boat speed. Drag depends on hull characteristics and speed. If the engine provides more torque than the propeller absorbs, the shaft speed will try to increase. This will produce more thrust and the boat will speed up. An equilibrium will be achieved between torque, thrust, drag and speed at a higher speed unless the governor on the engine prevents increased RPM. If the RPM can't increase, the boat can't reach the full speed potential of the engine and is "underwheeled". You may not want to accept this condition because it doesn t produce the deseired speed, but it is not harmful. Conversely, if the engine is unable to provide enough torque to turn the propeller, the shaft slows down, and thrust and speed drop, again to equilibrium. However, this "overwheeled" condition won't allow the engine to achieve full RPM and power, so the engine may smoke and lug and eventually suffer damage. This is especially a problem with turbocharged engines because they depend on aiir flow to cool the heads, and in the long run can be damaged by lugging. Note also that we need to know the engine characteristics as well. The amount of either power or torque available varies with RPM. The data for a specific engine is generally available from the manufacturer. However, read the rating conditions carefully for an engine as well. The full power or RPM may not be available for more than a short time, for example. Matching a propeller, gear and engine means that the equilibrium between the available engine torque and the required propeller torque will not overload the engine and that the thrust required to make speed is available throughout the range of operation

20 E Marine Training - Prop Matching - February, Strategy Full Load Vs Part Load Range/Efficiency Vs Top Speed Getting Onto Plane/Top Speed Mixed Service Towing, Trawling, Special Cases Speed Vs Towing Power Economic Analysis Probabilistic Voyage Simulation May Be Required For Fishing or Towing A boat is not generally just required to make top speed on trials day. The owner will generally want a long-lived, fuel efficient match to some specific mission profile (even if he doesn t know it). It is important to fully understand the required mission for a boat before deciding how to prop it. Often range or fuel efficiency may be better with some prop other than the one that gives the highest top speed. A common case for recreational boats is a good hole shot prop, for skiboats. A prop that works best at top end may require everything an engine has to accelerate because it is overloading the engine at lower speeds. The boat thus will accelerate slowly and not be as useful for waterskiing. A prop that is sized differently will have more low speed thrust by letting the engine run up more but won t have as high a top speed. Boats that tow fishing gear or other vessels require some additional thought, because there is generally a conflict between towing performance and top speed. A fishing vessel may need to get to and from the ground quickly, but then tow well. Rescue vessels have to get on site very quickly, and often execute a long difficult tow. Sailing yachts need to balance good speed and possibly range under power with the possible need to power into a heavy blow and to maneuver smartly in confined spaces. This also has to be balanced against the loss of speed under sail. Dinner cruise vessels usually don t need lots of speed, but do need plenty of thrust to dock in a bad blow. In the case of commercial vessels, you need to be ready to do at least simple economic studies, such as how much fuel savings is required to pay off a loan to buy a new prop, and spreadsheet programs offer numerous financial calculation tools to do theses studies. The most sophisticated tool for such studies are probably voyage simulation studies. These are programs that essentially do simple simulations of a voyage, but have randomizers to vary weather, fishing conditions or whatever. They are run hundreds of time to determine the average, best and worse possibilities, and are used to evaluate the economic (or military) effectiveness of just such features as propeller choice. (Or sailing yacht designs in the America s Cup.) The bottom line is that prop matching requires judgment as well as just calculation.

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